The spin dynamics of an anisotropic fermi supefluid (3He?)

In this paper we develop a general theory of the spin dynamics of anisotropic Fermi superfluids of the generalized BCS type, under conditions which should be realistic for any such phase of liquid ³He occurring below 3 mK. No restrictions are placed on the nature of the pairing configuration. The system is described in terms of the total spin vector S, and a vector T(n) which describes the amplitude and spin quantization axes of the pairs forming at a given point n on the Fermi surface; the kinematic relations between these quantities are emphasized. An approximation of the Born-Oppenheimer type is used to derive the general equations of motion of S and T; it is pointed out that relaxation of T due to collisions is inhibited by the coherent nature of the superfluid state. The equations of motion are solved for the particular case of unsaturated c.w. resonance, and it is shown that the nature of the transverse (usual) resonance spectrum is a strong function of the kind of configuration occurring; in particular, either one or two finite-frequency resonances may occur, depending on the configuration. A resonance is also predicted to occur when the r.f. field is polarized along the static external field. Specific predictions of the form of the transverse and “longitudinal” spectra are made for all the unitary l = 1 states, and it is shown that these predictions are unaffected by renormalization effects. The “Balian-Werthamer” state is predicted to show a longitudinal resonance but no transverse shift. The theory is compared with other approaches to the problem and its relevance to the anomalous low-temperature phases of liquid ³He is discussed.     

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements

We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k _F → 4k _F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.     

Fermi Surface Topology in the Case of Spontaneously Broken Rotational Symmetry

The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f(p, p') having a sharp peak at |p ? p'| = q₀. It is shown that, in the case of attraction and q₀ = 2p_F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q₀, the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ? π(p_F/q₀ ? 1) small hole pockets at the distance p_F ? q₀ from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L. At q₀ → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.     

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-T _c superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature ??strange metal phase?? of the doped Mott insulator.     

Asymmetric Tunneling Conductance and the Non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.     

Pseudogap behavior in the emery model for the electron-doped superconductor Nd2 − x Ce x CuO4: Multiband LDA + DMFT + Σk approach

We propose a generalization of the LDA + DMFT + Σ _k approach to the multiband case, in which correlated and uncorrelated states are present in the model simultaneously. Using the multiband version of the LDA + DMFT + Σ _k approach, we calculate the density of states and spectral functions for the Emery model in a wide energy interval around the Fermi level. We also obtain the Fermi surfaces for the electron-doped high-temperature superconductor Nd_{2 ? x} Ce _x CuO₄ in the pseudogap phase. The self-energy part Σ _k introduced additionally to take into account pseudogap fluctuations describes the nonlocal interaction of correlated electrons with collective Heisenberg short-range spin fluctuations. To solve the effective impurity model, the numerical renorm-group (NRG) method is used for the DMFT equations. Good qualitative agreement of the Fermi surfaces calculated using the LDA + DMFT + Σ _k approach and experimental angle-resolved photoemission spectroscopic data is attained. The stability of the dielectric solution with charge transfer in the Emery model with correction for double counting is analyzed in the Appendix.     

Surface instability of a nuclear fermi liquid drop

A mechanical instability of an incompressible Fermi liquid drop with respect to surface distortions is considered. It is shown that the Fermi surface distortion (FSD) reduces the instability-growth rate for surface fluctuations due to its effects on both the viscosity and the increase in the stiffness coefficient. The dependence of the limiting temperature T_lim on the mass number and the multipolarity of the nuclear-surface distortion is calculated. It is shown that T_lim is not influenced by the FSD effect.     

Charge-density-wave partial gap opening in quasi-2D KMo6O17 purple bronze studied by angle resolved photoemission spectroscopy

Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo₆O₁₇ purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ∼40 K well below the Peierls transition temperature for this material, with CDW transition temperature T_CDW ∼120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative k_F point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, E_F, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K_0.3MoO₃ blue bronze.     

Anomalous attenuation of longitudinal ultrasound in the intermediate state of pure type I superconductor

The dependence of ultrasonic attenuation on the direction of magnetic field H (H ⊥ k) in intermediate state of very pure gallium at T = 0.5°K was found to be anomalously different from the dependence observed at the same temperature and H = H_c in normal state. This phenomenon can be explained taking into account the anisotropy of the gallium Fermi surface.     

From the Bose-Einstein to fermion condensation

The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M _FC ^* and M _L ^* and intersecting near the binding energy E₀, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E₀ persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as \(M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). The regime is restored at some temperature \(T^ * \propto \sqrt B \). The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.     

Electron-electron interactions in the 2D electron system

In this paper, we report studies of the electron-electron interaction effects in 2D electron systems. The interaction manifests in renormalization of the effective spin susceptibility, effective mass, g^∗-factor, conductivity etc. By applying in-plane magnetic field, we tuned the effective interaction between the electrons and compared with theory the temperature dependence of the conductivity. We find a good agreement with interaction corrections calculated within the Fermi liquid theory. To address the question on the origin of the metal-insulator transition (MIT) in 2D, we explored transport and magnetotransport properties in the vicinity of the MIT and compared our data with solutions of two equations of the renormalization group (RG) theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the ρ(T,B_∥) data and the RG-theory in a wide range of the in-plane fields. These results support the Fermi liquid type origin of the metallic state and the interpretation of the observed 2D MIT as the true quantum phase transition.     

Effects of electron interaction on the change in sound velocity under de Haas-van Alphen conditions

Based on a temperature propagator technique in the grand ensemble of an interacting electron gas, the oscillatory sound velocity is examined under the de Haas-van Alphen conditions. In consideration of the oscillation of the Fermi energy (chemical potential) and the first order exchange effects, the dHvA oscillations of the sound velocity are shown to have the same one phase as in the case of an ideal electron gas, in agreement with experimental results. For large electron density, that is, for very small r_s, and by a proper renormalization of the Fermi energy, we have succeeded in eliminating one of the two oscillatory functions which have a phase difference of $\text{π}\text{2}$.     

Anomalous behavior of the surface tension at the interface of the metallic and insulating phases in the vicinity of the metal-insulator phase transition in a magnetic field

Mean-field equations describing the metal-insulator (MI) transition are formulated. They involve two coupled order parameters characterizing this transition: (i) a scalar order parameter describing the density change accompanying the transition from the insulating state to the metallic one and (ii) an order parameter (a two-component vector) describing the electron density in the metallic or semimetallic phase affected by the applied magnetic field. Two components of this vector correspond to different possible spin states of electrons in the applied magnetic field. The transition in the density of metallic and insulating phases being a first order phase transition is treated in terms of the Cahn-Hilliard-type gradient expansion. The transition in the electron density is a second order phase described by the Ginzburg-Landau-type functional. The coupling of these two parameters is described by the term linearly dependent on the electron density n in the metal with the proportionality factor being a function of the density of the metallic phase. The derived equations are solved in the case of the MI interface in the presence of both parallel and perpendicular uniform magnetic fields. The calculated surface tension Σ_mi between the metallic and insulating phases has a singular behavior. In the limit of zero electron density n ? 0, Σ_mi ～ n ^3/2. Near the MI transition point T _c(h) in the applied magnetic field, Σ_mi ～ [T - T _c(h)]^3/2. The singular behavior of the surface tension at the MI interface results in the clearly pronounced hysteresis accompanying the transition from the insulating to metallic state and vice versa.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

QCD at a Finite isospin density: From the pion to quark-antiquark condensation

QCD at a finite isospin chemical potential μ _I is studied. This theory has no fermion-sign problem and can be simulated on a lattice by using present-day techniques. We solve this theory analytically in two limits: low μ _I, where chiral perturbation theory is applicable, and asymptotically high μ _I, where perturbative QCD is at work. At a low isospin density, the ground state is a superfluid pion condensate. At a very high density, it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pions. Motivated by this observation, we put forward a conjecture that the transition from hadron to quark matter is smooth. The conjecture passes several nontrivial tests. Our results imply a nontrivial phase diagram in the space of the temperature and chemical potentials of isospin and baryon number. At asymptotically large values of μ _I and small values of the baryon chemical potential, the ground state is in a phase similar to the Fulde-Ferrell-Larkin-Ovchinnikov phase. It is characterized by a spatially modulated superfluid order parameter 〈ūγ ₅ d〉 and may be the asymptotic limit of the inhomogeneous pion-condensation phase advocated by Migdal and others.     

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of ¹⁷³Yb atoms near an orbital Feshbach resonance (OFR), where a single moving particle in the ³P₀ state interacts with two background Fermi seas of particles in different nuclear states of the ground ¹S₀ manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.     

Behavior of Fermi systems approaching the fermion condensation quantum phase transition from the disordered phase

The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M* diverges as M* ∝ 1/¦x?x_FC¦, where x is the system density and x_FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M* is finite, the system exhibits the Landau Fermi liquid behavior. At ¦x? x_FC¦/x_FC?1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦x–x_FC¦/x_FC?1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.     

Generalized susceptibilities and phonon anomalies in Pd and Pt metals

The generalized susceptibility, χ(q), in Pd and Pt for q along the [100], [110], [111], and [120] directions was determined from their APW and RAPW energy band structures, respectively, using the analytic tetrahedron linear energy scheme of Rath and Freeman. The band structures were previously found to yield Fermi surface radii, temperature dependencies of the static magnetic susceptibility, χ(T), resistivity, and a spin lattice relaxation, T₁T, in very good agreement with experiment. In the χ(q) calculations, we used 2048 tetrahedra in 1/48th irreducible BZ and the energy eigenvalues for bands 4, 5, and 6 which cross the Fermi energy as fitted to a Fourier series representation. The intraband parts of χ(q) at q = 0 for both metals are found to agree with the density of states at the Fermi energy to without 0.5%. Our results show that the dominant contribution to χ_intra arises from the dominant band 5 whose “jungle-gym” FS has strong nesting features; the main peak for Pd occurs at the same q value (= 0.65π/a) for q along the [0q0], [q, q, 0], and [q, q, q] directions. The locus of this main peak is a square in the (0, 0, 1) plane. The maximum of χ_intra for q along the [110] and [111] directions are 23% and 13%, respectively, higher than the value of χ(q) at q = 0. For q along the [010] and [120] directions, the peak is, however, lower than the value of χ_intra at q = 0. Hence, while phonon anomalies are predicted for the [110] and [111] directions, no anomaly is predicted for either the [100] or [120] direction. The predicted q value for the [110] anomaly, $\text{q}\text{= 0.65π/a}$ is close to the experimental value of ～0.7 π/a. Although there may be a hint of an anomaly at 0.56 [111] in the measurements, a more detailed investigation of this region is called for. For platinum, χ_intra for q along the [010], [110] and [111] directions has main peaks which occur at q = 0.68 π/a, 0.75 π/a, and 0.85 π/a, respectively. Here too, this main peak comes from the nesting of the jungle-gym Fermi surface which is not, however, as flat as that of palladium. Anomalies are predicted (although weaker in Pt than in Pd) along [110] and [111] but not along [100] and [120]. The [110] anomaly is close to the measured q value (～0.7–0.8 π/a). Also in agreement with experiment, we predict a weaker [110] anomaly for Pt than for Pd. In both Pd and Pt, weaker anomalies are predicted for the [111] direction than for the [110] direction.     

General properties of a magnetic-field-induced landau Fermi liquid in high-temperature superconductors and heavy fermion metals

It has been shown that the magnetic-field-induced transition from a non-Fermi-liquid state to a Fermi liquid state in the Tl₂Ba₂CuO_{6 + x} high-temperature superconductor is similar to a transition observed in heavy fermion metals. This behavior is explained in the theory of the Fermi condensate quantum-phase transition implying the existence of Landau quasiparticles. The Fermi condensate quantum-phase transition can be considered as a universal cause of the strongly correlated behavior observed in various metals and liquids such as high-temperature superconductors, heavy fermion metals, and two-dimensional Fermi systems.